ALMOST SURE LIMIT DISTRIBUTIONS OF THE INCREMENTS FOR PROCESSES WITH EXCHANGEABLE OR INDEPENDENT INCREMENTS

M. Wschebor ([6], [7]) has proved that if X(t) is a process with independent and stationnary increments without gaussian part there it exists a function a (h) decreasing on R(+) such that if we denote by mu(h) the measure defined by mu(h) (B) = lambda {t, t epsilon [0, 1], X(t+h) - X(t)/alpha (h) epsilon B} mu(h) converges a.s. [property denoted by (*)] iff the Levy measure has the property of regular variation [3], and the limit mu is a stable law. Here, we are interested to the case of processes with exchangeable increments [5]. These processes, suitably normed form a compact convex set of probability measures on D (0, 1). They are a linear combination of a translation process, a brownian bridge and processes given by: [GRAPICS] where (U-j)(j epsilon N)* is a sequence of independent and uniform variables, alpha = (alpha(j)) is a sequence of r.v., independent of (U-j), such that [GRAPHICS] ch that [GRAPHICS] llulatum segments in these translocations were determined by in situ hybridization analysis using total genomic T. umbellulatum DNA as a probe